Temperature-measuring method and distributed optical fiber temperature sensor

ABSTRACT

A temperature-measuring method which comprises inputting laser pulses into an optical fiber to be measured and measuring the temperature distribution in the fiber from the ratio of the amplitudes and the delay time of the Stokes light and the anti-Stokes light contained in the return beam from the optical fiber, wherein the temperature distribution is measured by using an equation: ##EQU1## where T(x) is the temperature to be measured, Θ is the reference temperature, R&#39;(T) is the relative ratio of amplitude to the measuring point, R&#39;(Θ) is the relative ratio of amplitude at the reference temperature point, k is the Boltzmann&#39;s constant, h is the Planck&#39;s constant, c is the velocity of light, ν is the Raman shift, α is the attenuation difference in the optical fiber between the Stokes light and the anti-Stokes light, and x is the distance, wherein the attenuation differenct α is represented by a function α{T(τ)} which is dependent on the temperature T(τ) at the measuring point τ, and the exponential function in which the exponential part is represented by a value obtained by integrating the function α{T(τ)} with the variation dτ in distance, is employed as a correction factor.

BACKGROUND OF THE INVENTION

The present invention relates to a temperature-measuring methodemploying a distributed optical fiber temperature sensor. Moreparticularly, it relates to a distributed optical fiber temperaturesensor and a temperature-measuring method, whereby the influence of theattenuation difference in the optical fiber to be measured, whichcreates a problem when the ratio of the Stokes light and the anti-Stokeslight is taken, is corrected so that the temperature distribution in along distance optical fiber can be measured with high precision.

A block diagram of a conventional distributed optical fiber temperaturesensor is shown in FIG. 5. Laser pulses, generated from a laser pulser10 of a light source, are input into an optical fiber 12 to be measured,and Raman back scattered light generated in the optical fiber 12 isreturned to the incident end. Such Raman back scattered light will beintroduced by an optical directional coupler 11 to a measuringapparatus, whereby the Stokes light and the anti-Stokes light in theRaman back scattered light are separated by a filter 13, detected, andconverted, respectively, to electrical signals in proportion to theirassociated amplitudes by the respective photo-electric converters 14 and14'. Such electrical signals are amplified by the respectivepreamplifiers 15 and 15' and subjected to a prescribed number ofaveraging treatment operations by an averager 16. The resultingaverage-treated signal is transmitted to a signal processing unit 17,whereby the delay time and the ratio of the amplitudes of the Stokeslight and the anti-Stokes light are calculated, and the temperaturedistribution is output.

In the calculation of the ratio of the amplitudes of the Stokes lightand the anti-Stokes light, it is difficult to obtain the ratio of theabsolute amplitudes. Therefore, the ratio of the amplitudes of thestokes and anti-stokes light is obtained from the ratio of the relativeamplitudes (hereinafter sometimes referred to as "the relative ratio ofamplitudes") by the following equation by Dakin (Dakin, J. P. Pratt, D.J., Bibby, G. W., Ross, J. N. "Temperature distribution measurementusing Raman ratio thermometry", SPIE Vol 566, Fiber Optic and LaserSensors III 249 (1985)): ##EQU2## In the above equation, T is thetemperature to be measured, Θ is the reference temperature at areference measuring point, R'(T) is the relative ratio of amplitudes atthe measuring point, R'(Θ) is the relative ratio of amplitudes at thereference temperature point, k is the Boltzmann's constant, h is thePlanck's constant, c is the velocity of light, and ν is the Raman shift.

The incident laser pulses from the light source, such as a semiconductorlaser, naturally undergo attenuation during transmission through theoptical fiber to be measured. The influence of this attenuation can beavoided by taking the ratio of the Stokes light and the anti-Stokeslight. However, the influence of the attenuation difference between theStokes light and the anti-Stokes light, when the Raman scattering isgenerated by the incident wave and the scattered light is transmittedbackwards, can not be avoided simply by taking the ratio. Therefore, acorrection is required which takes the influence of this attenuationdifference into consideration. If such a correction is not conducted,even if a uniform temperature distribution is measured, a substantiallyinclined temperature distribution will be output as shown in FIG. 4.Further, the attenuation difference itself has a temperature dependency,and the influence of the temperature dependency will be substantial inthe case of a measurement taken over a long distance. As a result,accurate measurement with a high precision has been difficult to obtain.

SUMMARY OF THE INVENTION

The present invention has been made to solve the above mentionedproblems. According to a first embodiment, the present inventionprovides a temperature-measuring method which comprises inputting laserpulses into an optical fiber to be measured and measuring thetemperature distribution in the fiber from the ratio of the amplitudesand the delay time of the Stokes light and the anti-Stokes lightcontained in a return beam emitted from the optical fiber. Thetemperature distribution is measured by using an equation: ##EQU3##wherein T(x) is the temperature to be measured, Θ is the referencetemperature, R'(T) is the relative ratio of amplitudes at the measuringpoint, R'(Θ) is the relative ratio of amplitudes at the referencetemperature point, k is the Boltzmann's constant, h is the Planck'sconstant, c is the velocity of light, ν is the Raman shift, α is theattenuation difference in the optical fiber between the Stokes light andthe anti-Stokes light, and x is the distance. In the equation, theattenuation difference α is represented by a function α{T(τ)} which isdependent on the temperature T(τ) at the measuring point τ, and theexponential function, in which the exponential part is represented by avalue obtained by integrating the function α{T(τ)} with the variation dτin distance, is employed as a correction factor.

According to a second embodiment, the present invention provides atemperature-measuring method which comprises inputting laser pulses intoan optical fiber to be measured, and measuring the temperaturedistribution in the optical fiber from the ratio of the amplitudes andthe delay time of the Stokes light and the anti-Stokes light containedin the return beam from the optical fiber. The temperature distributionis measured by using first and second correction equations as set forthbelow.

First correction equation ##EQU4##

In the first correction equation, T(x) is the temperature to bemeasured, Θ is the reference temperature, R'(T) is the relative ratio ofamplitudes at the measuring point, R'(Θ) is the relative ratio ofamplitudes at the reference temperature point, k is the Boltzmann'sconstant, h is the Planck's constant, c is the velocity of light, ν isthe Raman shift, α is the attenuation difference in the optical fiberbetween the Stokes light and the anti-Stokes light, x is the distance,and u is a real number of at least 0, wherein the attenuation differenceα is represented by a constant value, and the exponential function, inwhich the exponential part is the product of the attenuation differenceα and the distance x, is employed as a correction factor.

Second correction equation ##EQU5##

In the second correction equation, T(x), Θ, R'(T), R'(Θ), k, h, c, ν, αand x are as defined above with respect to the first correctionequation, wherein the attenuation difference α is represented by afunction α{T(τ)} which is dependent on the temperature T(τ) at themeasuring point τ, and the exponential function, in which theexponential part is represented by a value obtained by integrating thefunction α{T(τ)} with the variation dτ in distance, is employed as acorrection factor. In this second embodiment, the temperaturedistribution [T_(n) ⁰ ], (wherein n is an integer of at least 1)obtained by the first correction equation, is substituted into theexponential part of the second correction equation, to obtaintemperature distribution [T_(n) ¹ ]. Subsequently, temperaturedistribution [T_(n) ^(r) ], (wherein r is an integer of at least 1)obtained immediately before, is successively substituted into the secondcorrection equation, to obtain temperature distribution [T_(n) ^(r+1) ]at r+1 times. As a result, the temperature distribution [T_(n) ^(r) ],obtained when the error ##EQU6## (wherein m is the number of themeasuring points) becomes not higher than a predetermined value at rtimes, is taken as the measured value.

According to a third embodiment, the present invention provides adistributed optical fiber temperature sensor which comprises a lightsource which inputs laser pulses into an optical fiber to be measured,an optical directional coupler which introduces the return beam from theoptical fiber to a signal processing unit, and a signal processing unitwhich detects the Stokes light and the anti-Stokes light contained inthe return beam and which measures the temperature distribution in theoptical fiber from the ratio of the amplitudes and the delay time of theStokes light and the anti-Stokes light. In this third embodiment, thesignal processing unit measures the temperature distribution by using anequation: ##EQU7## wherein T(x) is the temperature to be measured, Θ isthe reference temperature, R'(T) is the relative ratio of amplitudes atthe measuring point, R'(Θ) is the relative ratio of amplitudes at thereference temperature point, k is the Boltzmann's constant, h is thePlanck's constant, c is the velocity of light, ν is the Raman shift, αis the attenuation difference in the optical fiber between the Stokeslight and the anti-Stokes light, and x is the distance.

According to a fourth embodiment, the present invention provides adistributed optical fiber temperature sensor which comprises a lightsource which inputs laser pulses into an optical fiber to be measured,an optical directional coupler which introduces the return beam from theoptical fiber to a signal processing unit, and a signal processing unitwhich detects the Stokes light and the anti-Stokes light contained inthe return beam and which measures the temperature distribution in theoptical fiber from the ratio of the amplitudes and the delay time of theStokes light and the anti-Stokes light, In this fourth embodiment, thesignal processing unit measures the temperature distribution by usingfirst and second correction equations as set forth below.

First correction equation ##EQU8##

In this first correction equation, T(x) is the temperature to bemeasured, Θ is the reference temperature, R'(T) is the relative ratio ofamplitudes at the measuring point, R'(Θ) is the relative ratio ofamplitudes at the reference temperature point, k is the Boltzmann'sconstant, h is the Planck's constant, c is the velocity of light, ν isthe Raman shift, α is the attenuation difference in the optical fiberbetween the Stokes light and the anti-Stokes light, x is the distance,and u is a real number of at least 0, wherein the attenuation differenceα is represented by a constant value, and the exponential function, inwhich the exponential part is the product of the attenuation differenceα and the distance x, is employed as a correction factor.

Second correction equation ##EQU9##

In the second correction equation, R(x), Θ, R'(T), R'(Θ), k, h, c, ν, αand x are as defined above, with respect to the first correctionequation, the attenuation difference α is represented by a functionα{T(τ)} which is dependent on the temperature T(τ) at the measuringpoint τ, and the exponential function, in which the exponential part isrepresented by a value obtained by integrating the function α{T(τ)} withthe variation dτ in distance, is employed as a correction factor. Inthis fourth embodiment, the temperature distribution [T_(n) ⁰ ] (whereinn is an integer of at least 1), obtained by the first correctionequation, is substituted into the exponential part of the secondcorrection equation, to obtain temperature distribution [T_(n) ¹ ].Subsequently, temperature distribution [T_(n) ^(r) ] (wherein r is aninteger of at least 1) obtained immediately before is successivelysubstituted into the second correction equation, to obtain temperaturedistribution [T_(n) ^(r+1) ] at r+1 times, and temperature distribution[T_(n) ^(r) ] obtained, when the error ##EQU10## (wherein m is thenumber of the measuring points), becomes not higher than a predeterminedvalue at r times, is taken as the measured value.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings,

FIGS. 1a, b to 3a, b are graphs showing the results of the measurementsconducted by the method and the sensor of the present invention.

FIG. 4 is a graph showing the results of measurement conducted by aconventional method.

FIG. 5 is a block diagram of a conventional sensor.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Now, the present invention will be described in detail with reference tothe preferred embodiments.

In the first and third embodiments of the present invention, theexponential function of the correction factor is determined by thefollowing procedure.

For instance, 1 km of an optical fiber to be measured is divided into100 measuring points with an interval of every 10 m. At the firstmeasuring point x=1, the temperature T(1) is calculated by the equationcontaining no correction factor. The temperature T(2), at the secondmeasuring point x=2, can be obtained approximately by introducing theattenuation difference α{T(1)} obtained from the temperature measured atthe first measuring point into the correction factor, since the error isnegligible. Further, the temperature T(3), at the third measuring pointx=3, can likewise be obtained by introducing the attenuation differenceα{T(1)} at the first measuring point and the attenuation differenceα{T(2)} at the second measuring point into the correction factor.Accordingly, the correction factor C_(n) at the nth measuring point(where n is an integer of at least 1) i.e. at an optional distance x, isobtained by: ##EQU11## In this case, data of attenuation difference α ina temperature range of from about 0° C. to about 100° C. to which thesensor of the present invention will be applied, are memorized or storedby the signal processing unit prior to the measurement of thetemperature distribution and will be used for the measurement. Here, theattenuation difference α is determined by the following procedure. Whenthe temperature of the entire optical fiber is constant, the amplitudesignals I_(AS) (x) of the anti-Stokes light is represented by thefollowing equation:

    I.sub.As (x)=A(T)·e.sup.a(T)·x ;         (5)

where x is the distance, a(T) is the attenuation of the anti-Stokeslight at a temperature T, and A(T) is a function which is dependent onthe temperature. When natural logarithm is applied to both sides of theabove equation, the following equation (6) will be obtained:

    lnI.sub.As (x)=lnA(T)+a(T)·x                      (6)

Here, if the temperature T is constant against x, i.e., if thetemperature is constant over the entire optical fiber, equation (6) willbe a linear line with a slope of a(T) with lnA(T) being intercept.Accordingly, by changing the temperature T to various values andconducting the above treatment, the slopes a(T) at various temperaturescan be obtained. The attenuation b(T) of the Stokes light can beobtained in a similar manner. Accordingly, the attenuation differenceα(T) at a temperature T will be obtained by the following equation:

    α(T)=b(T)-a(T)(m.sup.-1).                            (7)

Further, as a result of extensive research, the present inventors havefound that α(T) can be approximated by a quadric curve relating to thetemperature T, and α(T) can be memorized as a quadric function of T,which can in turn be used for the calculation of the correction factorC_(n). Further, α(T) may vary slightly depending upon the type of theoptical fiber used, and in such a case, α(T) may be determined for eachtype of such optical fiber.

Now, the second and fourth embodiments of the present invention will bedescribed.

Firstly, the following treatment is conducted by setting u=0 or 1 in thefirst correction equation. However, the case where u=1 is preferred,since the measurement can thereby be conducted with high precision. Inthe case of u=1, the attenuation difference α is substituted as aconstant value corresponding to a certain temperature within atemperature range of from about 0° C. to about 100° C. in which thesensor of the present invention will be applied. In this case, if anoptical fiber of 1,000 m is divided into 1,000 measuring points, spacedevery 1 m, the temperature distribution ]T_(n) ⁰ ] (wherein n is aninteger of 1≦n≦1,000) is obtained with respect to the 1,000 measuringpoints. Also, in the case of u=0, [T_(n) ⁰ ] is obtained in a similarmanner. Then, the above temperature distribution is substituted into theexponential part of the second correction equation, i.e., by using theabove equation (3), calculation, by the following equation (8):##EQU12## is conducted with respect to n=1 to 1,000. The result isrepresented by [T_(n) ¹ ] (1≦n≦1,000). In equation (8), the sum of up ton terms is taken to increase the precision. Next, the error ε isobtained by the following equation: ##EQU13## If the error ε is largerthan the prescribed value e.g. 3, [T_(n) ¹ ] is further substituted intothe second correction equation to obtain [T_(n) ² ] (1≦n≦1,000). Thisoperation will then be repeated until the error ε becomes not higherthan the prescribed value, and the temperature distribution [T_(n) ^(r)], when the error ε becomes not higher than the prescribed value, istaken as the measured value. This operation may be represented by thefollowing equation (10):

    [T.sub.n.sup.r ]=f[T.sub.n.sup.r-1 ];                      (10)

where f[T_(n) ^(r-1) ] is the operation of substituting the previoustemperature distribution [T_(n) ^(r-1) ] into the exponential part ofthe right side of the second correction equation. Namely, the results ofthe left side are sequentially substituted into the right side, and theerror ε is determined until the desired value is obtained. In theforegoing instance, the measuring points are taken every 1 m, but themeasurement may be conducted for every 10 m or other length. Further, inthis case, the attenuation difference α of the exponential part of thesecond correction equation is taken in consideration of the temperaturedependency, and its data are memorized or stored by the signalprocessing unit prior to the measurement of the temperature distributionor they are memorized or stored in the form of a quadric function of thetemperature T, and will be used for the measurement of the temperaturedistribution.

In the present invention, a correction factor, based on the attenuationreference α of the Stokes light and the anti-Stokes light, is introducedinto the Dakin equation used for the measurement of the temperaturedistribution in the optical fiber, and the correction equation takingthe temperature dependency of the attenuation difference α intoconsideration is used, whereby in the temperature distributionmeasurement of an optical fiber of a long distance, the problem that thetemperature distribution curve inclines substantially due to thedistance, can be solved, and the measurement can be conducted with highprecision.

Now, the present invention will be described in further detail withreference to the following Examples. However, it should be understoodthat the present invention is by no means restricted to such specificExamples.

EXAMPLES

FIGS. 1 to 3 illustrate the Examples of the present invention.

FIG. 1(a) is a graph showing the temperature distribution obtained byusing the correction equation: ##EQU14## FIG. 1(b) is a graph of aReference Example wherein α is a constant value, and the exponentialpart is simply represented by αx. In FIG. 1(a), the temperaturedistribution is not substantially inclined as compared with theconventional instance of FIG. 4, and the precision is substantiallyimproved over the case of FIG. 1(b).

In this Example, an optical fiber of 1,000 m was measured at measuringpoints set every 1 m.

FIG. 2(a) is a graph showing the temperature distribution obtained bythe convergent method employing the first correction equation (u=1)having αx introduced into the exponential part and the second correctionequation, and it shows the results up to the second treatment i.e.,[T_(n) ² ]. FIG. 2(b) is a graph of a Reference Example wherein α is aconstant value, and the exponential part is simply represented by αx. InFIG. 2(a), the temperature distribution is not substantially inclined ascompared with the conventional instance of FIG. 4, and the precisionthereof is substantially improved over FIG. 2(b). In this Example, anoptical fiber of 1,000 m was measured at measuring points of every 1 m.In this Example, errors ε₁ to ε₆ obtained by the operations of 6 timesare as follows: ##EQU15## FIG. 2(a) shows a case wherein the operationwas terminated when the error became ε₂ ≦3. In the range of ε₃ or below,no difference was visually observed when compared with the graph in thecase of ε₂. The prescribed value to be used for the judgment of theerror ε is not limited to the above identified value 3 and may suitablybe selected.

FIG. 3(a) is a graph showing the temperature distribution obtained bythe convergent method employing the first correction equation (u=0)having no exponential part and the second correction equation, andrepresents the results up to the third treatment i.e., [T_(n) ² ]. FIG.3(b) is a graph of a Reference Example in which α is a constant value,and the exponential part is represented simply by αx. In FIG. 3(a), thetemperature distribution is not substantially inclined as compared withthe conventional instance of FIG. 4, and the precision is substantiallyimproved over FIG. 3(b). In this Example, an optical fiber of 1,000 wasmeasured at measuring points of every 1 m. In this Example, theoperation was terminated when the error become ε₃ ≦3, whereby theprecision was slightly lower than the case of FIG. 2(a). The slightlylower precision is believed to be attributable to the fact that noexponential part was introduced into the first correction equation.

Here, the sensor of the present invention is such that in theconventional apparatus as shown in FIG. 5, the treatment having theabove correction factor introduced is conducted by a signal processingunit i.e., a unit comprising a filter 13, photo-electric converters 14and 14', preamplifiers 15 and 15', an averager 16 and a signalprocessing section 17. More specifically, the treatment having the abovecorrection factor introduced, is conducted by the signal processingsection 17 or by a microcomputer connected to the signal processingsection 17.

The results of FIGS. 1 to 3 are those obtained by the measurementswherein α was 0.6×10⁻⁵ (m⁻¹), Θ was 25(°C.), R'(T) and R'(Θ) wereempirically obtained, k=1.38065800×10⁻²³ J·K⁻¹, h=6.62607550×10⁻³⁴ J·S,c=2.99792458×10⁸ m·s⁻¹, and ν=440 (cm⁻¹).

Further, ν may have a varied value or may be an empirically obtainedreal value. The adverse effect to the relative ratio of the Stokes lightand the anti-Stokes light caused by the optical connection between therespective units in the sensor system of the present invention, may becorrected by subjecting the signal processing unit to off settingadjustment by means of a new correction factor δ as shown below, priorto the measurement: ##EQU16##

As described in the foregoing, according to the present invention,treatment is conducted based on an equation having a correction factorintroduced to the conventional Dakin equation and further a correctionequation taking the temperature dependency of the attenuation differenceα in the correction factor into consideration, is employed, whereby theconventional problem such that the entire curve of the temperaturedistribution substantially inclines with distance, can be solved, andthe precision in the temperature measurement for a long distance can beimproved.

We claim:
 1. A temperature-measuring method which comprises the stepsof:maintaining a reference point of an optical fiber at a knownreference temperature; inputting laser pulses into an incident end ofthe optical fiber to be measured; detecting the amplitudes and delaytime of the Stokes and anti-Stokes light contained in a return beam fromthe optical fiber; and measuring the temperature distribution in thefiber from a ratio of respective amplitudes of said Stokes andanti-Stokes light and said delay time of the Stokes light and theanti-Stokes light contained in said return beam from the optical fiber,wherein the temperature distribution is measured by using an equation:##EQU17## where T(x) is the temperature to be measured at a measuringpoint, Θ is the reference temperature at a reference measuring point,R'(T) is the relative ratio of the amplitudes of the Stoke andanti-Stoke light of the return beam at the measuring point, R'(Θ) is therelative ratio of amplitudes of the Stoke and anti-Stoke light of thereturn beam at the reference temperature point, k is the Boltzmann'sconstant, h is the Planck's constant, c is the velocity of light, ν isthe Raman shift, α is an attenuation difference in the optical fiberbetween the Stokes light and the anti-Stokes light, and x is a distanceof the measuring point from the incident end of the optical fiber,wherein the attenuation difference α is represented by a functionα{T(τ)} which is dependent on the temperature T(τ) at the measuringpoint τ, and the exponential function in which the exponential part isrepresented by a value obtained by integrating the function α{T(τ)} withthe variation dτ in distance, is employed as a correction factor.
 2. Thetemperature-measuring method according to claim 1, wherein prior to themeasurement of the temperature distribution, α at various temperaturesis memorized by the signal processing unit.
 3. A distributed opticalfiber temperature sensor which comprises: means for maintaining atemperature reference point of an optical fiber at a known referencetemperature, a light source which inputs laser pulses into an incidentend of the optical fiber to be measured, an optical directional couplerwhich introduces a return beam from the optical fiber to a signalprocessing unit, and the signal processing unit, the signal processingunit including means for detecting the Stokes light and the anti-Stokeslight contained in the return beam and means for measuring thetemperature distribution in the optical fiber from the ratio of theamplitudes and the delay time of the Stokes light and the anti-Stokeslight, wherein said temperature distribution is obtained by using anequation: ##EQU18## where T(x) is the temperature to be measured at ameasuring point, Θ is the reference temperature at the referencetemperature point, R'(T) is the relative ratio of amplitudes of theStokes and anti-Stokes light at the measuring point, R'Θ is the relativeratio of amplitudes of the Stokes and anti-Stokes light at the referencetemperature point, k is the Boltzmann's constant, h is the Planck'sconstant, c is the velocity of light, ν is the Raman shift, α is anattenuation difference in the optical fiber between the Stokes light andthe anti-Stokes light, and x is a distance to the measuring point fromthe incident end of the optical fiber.
 4. The distributed optical fibertemperature sensor according to claim 3, wherein prior to themeasurement of the temperature distribution, α at various temperaturesis memorized by the signal processing unit.